Exemplary embodiments of the invention relate to kinematic ranging techniques.
Kinematic ranging per se is a known electronic counter-counter-measure technique, in which the range of a moving airborne jammer may be estimated by use of a radar unit without the need for the unit to actively interrogate the jammer, i.e. the radar unit may work in a passive mode to detect and process the jammer signals. In the specific examples of the invention described below, the radar unit is an airborne detecting radar unit. Kinematic ranging is described for example in “Kinematic Ranging for IRST”, SPIE Vol 1950, Acquisition, Tracking and Pointing VII (1993).
Referring to FIG. 1, in a known kinematic ranging technique, an airborne jammer moves along a trajectory 18 from a first position 10 to a second position 12 in a time interval Δt=t2−t1, during which an airborne detecting radar unit carries out a manoeuvre along a path 20 from a position 14 to a position 16, corresponding to a displacement 22 defined by displacement components Δx, Δy in the x and y directions respectively. The change Δα in azimuth bearing angle of the jammer with respect to the airborne detecting radar unit between the times t1 and t2 is given by
            Δ      ⁢                          ⁢      α        =                  α        1            +                                                  ⅆ              α                                      ⅆ              t                                ·          Δ                ⁢                                  ⁢        t            -              α        2              ;where α1 and α2 are the bearings in azimuth of the jammer at times t1 and t2 with respect to positions 14 and 16 respectively. The angle Δβ between the straight line connecting positions 14 and 10 and the displacement 22 is given by
                              Δ          ⁢                                          ⁢          β                =                              π            2                    -                      arctan            ⁢                                                  ⁢                                          Δ                ⁢                                                                  ⁢                y                                            Δ                ⁢                                                                  ⁢                x                                              -                      α            1                    -                                                                      ⅆ                  α                                                  ⅆ                  t                                            ·              Δ                        ⁢                                                  ⁢                          t              .                                                          (                  Equation          ⁢                                          ⁢          1                )            
Δβ is the angle in the azimuthal plane between the straight line joining the position of the airborne detector radar at time t1 and the position of the jammer at t2 and the straight line corresponding to the displacement of the airborne detector radar during the interval Δt. Using the sine rule, the range R of the jammer from the airborne detecting radar at time t2 is given by
                              R                      sin            ⁢                                                  ⁢            Δ            ⁢                                                  ⁢            β                          =                                                                              Δ                  ⁢                                                                          ⁢                                      x                    2                                                  +                                  Δ                  ⁢                                                                          ⁢                                      y                    2                                                                                      sin              ⁢                                                          ⁢              Δ              ⁢                                                          ⁢              α                                .                                    (                  Equation          ⁢                                          ⁢          2                )            
The range R of the jammer from the second position 16 of the airborne detecting radar may be therefore be calculated by measuring the bearings α1, α2 in azimuth of the jammer at the times t1, t2 with respect to the airborne detecting radar unit, the rate of change dα/dt of the bearing in azimuth of the jammer with respect to the position 14, the components Δx, Δy of the displacement 22 corresponding to the manoeuvre 20 of the airborne detecting radar, and the time interval Δt.
A disadvantage of the known method of kinematic ranging is that when the airborne detecting radar unit carries out a general manoeuvre 20, corresponding to a general displacement such as 22, the final result for the range R typically involves a significant level of uncertainty as a result of measurement errors associated with the values of α1, α2, dα/dt, Δt, Δx and Δy.
The present invention provides a method of kinematic ranging comprising the steps of:                (i) measuring the bearing α1 in azimuth of a jammer at a time t1 with respect to a first position using an airborne radar detector located at the first position;        (ii) measuring the rate of change dα/dt of the bearing in azimuth of the jammer with respect to the first position using the airborne radar detector located at the first position;        (iii) causing the airborne radar detector to carry out a manoeuvre such that it is displaced to a second position by a horizontal displacement d having orthogonal components Δx, Δy in a time Δt=t2−t1 and measuring the bearing α2 in azimuth of the jammer at time t2 with respect to the second position using the airborne radar detector located at the second position, where d=√{square root over (Δx2+Δy2)};        (iv) calculating the difference Δα in the bearing in azimuth of the jammer between the second and first positions;characterised in that the components Δx, Δy are calculated by the steps of:        (a) choosing a desired relative range accuracy σR/R for the method;        (b) obtaining an estimated range Rest of the jammer from the second position at time t2;        (c) finding d on the basis of the relative range accuracy, the estimated range Rest, the variance σΔα2 in Δα and the variance σd2 in d according to        
      σ    R    =            R      d        ⁢                                        (                                          R                2                            -                              d                2                                      )                    ·                      σ                          Δ              ⁢                                                          ⁢              α                        2                          +                  σ          d          2                                    (d) calculating the components Δx, Δy of the displacement d according toΔx=cos(α1+{dot over (α)}·Δt)·d Δy=−sin(α1+{dot over (α)}·Δt)·d         
and also characterised in that the range R of the jammer from the second position is calculated according to
  R  =            d              sin        ⁢                                  ⁢        Δ        ⁢                                  ⁢        α              .  
The invention provides the advantage that the range R may be measured with a desired relative range accuracy by causing the airborne radar detector to carry out the manoeuvre d having the calculated displacement components Δx, Δy in the horizontal plane.
In order to provide the possibility of a further increase in the accuracy of the determined range R, preferably the method further comprises the steps of                (i) evaluating the angle Δβ1 between the straight line joining the first position of the airborne detector radar and the position of the jammer at time t2, and the straight line defined by the components Δx, Δy;        (ii) evaluating the angle Δβ2 between the straight line joining the first position of the airborne detector radar and the position of the jammer at time t2, and the straight line defined by the components −Δx, Δy;        (iii) if |Δβ1−π/2|≦|Δβ2−π/2| then choosing the manoeuvre of the airborne detector radar such that its displacement has components Δx, Δy and if |Δβ1−π/2|>|Δβ2−π/2| then choosing the manoeuvre of the airborne detector radar such that its displacement has components −Δx, Δy.        
In some embodiments, the method may be applied to the simultaneous determination of the range of two jammers, in which case the method preferably further includes the steps of:                (i) evaluating the angle Δβ11 between the straight line joining the first position of the airborne detector radar and the position of the first jammer at time t2, and the straight line defined by the components Δx, Δy;        (ii) evaluating the angle Δβ12 between the straight line joining the first position of the airborne detector radar and the position of the second jammer at time t2, and the straight line defined by the components Δx, Δy;        (iii) evaluating the angle Δβ21 between the straight line joining the first position of the airborne detector radar and the position of the first jammer at time t2, and the straight line defined by the components −Δx, Δy;        (iv) evaluating the angle Δβ22 between the straight line joining the first position of the airborne detector radar and the position of the second jammer at time t2, and the straight line defined by the components −Δx, Δy;        (v) if |Δβ11+Δβ12−π|≦|Δβ21+Δβ22−π| then choosing the manoeuvre of the airborne detector radar such that its displacement has components Δx, Δy and if        |Δβ11+Δβ12−π|>|Δβ21+Δβ22−π| then choosing the manoeuvre of the airborne detector radar such that its displacement has components −Δx, Δy.        
This ensure the greatest overall accuracy in the determined ranges of the two jammers.